Multiple Solutions for a Nonlocal Anisotropic Schrödinger–Kirchhoff System with Applications to Mining Excavation Stability
- 1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
- 2Research Unit Geometry, Algebra, Analysis and Applications, Mathematics and Computer Sciences Department, Faculty of Science and Technology, University of Nouakchott, Nouakchott P.O. Box 5026, Mauritania
Abstract
This paper studies the existence of multiple weak solutions for a Schrödinger–Kirchhoff-type elliptic system driven by nonlocal anisotropic variable exponent operators. The model combines anisotropic μ(·)-Laplacian-type diffusion, Kirchhoff nonlocal terms depending on global energy integrals, and nonlinear potential effects on RN. The analysis is carried out in anisotropic variable exponent Sobolev spaces, and the main result is obtained via variational methods based on Ricceri’s three critical points theorem. As an application, the theoretical framework is used to investigate the stability of underground excavations in geologically heterogeneous mining formations, where the anisotropic exponents capture direction-dependent rock resistance and the Kirchhoff terms model strain-dependent stiffness; a numerical example illustrates the existence of multiple equilibrium states and identifies a critical loading threshold separating single- and multiple-equilibrium regimes.
Related
- Systems of Kirchhoff quasilinear Schrodinger equations with Hardy potential and critical Choquard-type nonlinearity
- Least energy sign-changing solutions for asymptotically cubic Kirchhoff equations on locally finite graphs
- Ground state solutions and asymptotics for discrete Kirchhoff problems
- Multiplicity of normalized solutions for the L2-supercritical Kirchhoff equation with partial confinement
- Existence and multiplicity of solutions for mixed local and nonlocal Kirchhoff type problems
BibTeX
@article{kefi2026multiple,
title = {{Multiple Solutions for a Nonlocal Anisotropic Schrödinger–Kirchhoff System with Applications to Mining Excavation Stability}},
author = {Khaled Kefi and Ahmed Ahmed},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193567},
url = {https://www.mdpi.com/2227-7390/14/19/3567},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Multiple Solutions for a Nonlocal Anisotropic Schrödinger–Kirchhoff System with Applications to Mining Excavation Stability
AU - Khaled Kefi
AU - Ahmed Ahmed
PY - 2026
DA - 2026/10/01
JO - Mathematics
DO - 10.3390/math14193567
UR - https://www.mdpi.com/2227-7390/14/19/3567
AB - This paper studies the existence of multiple weak solutions for a Schrödinger–Kirchhoff-type elliptic system driven by nonlocal anisotropic variable exponent operators. The model combines anisotropic μ(·)-Laplacian-type diffusion, Kirchhoff nonlocal terms depending on global energy integrals, and nonlinear potential effects on RN. The analysis is carried out in anisotropic variable exponent Sobolev spaces, and the main result is obtained via variational methods based on Ricceri’s three critical points theorem. As an application, the theoretical framework is used to investigate the stability of underground excavations in geologically heterogeneous mining formations, where the anisotropic exponents capture direction-dependent rock resistance and the Kirchhoff terms model strain-dependent stiffness; a numerical example illustrates the existence of multiple equilibrium states and identifies a critical loading threshold separating single- and multiple-equilibrium regimes.
SN - 2227-7390
ER -